A relationship between two quantitative or qualitative variables is considered significant according to the χ² (Chi-square) test at which of the following levels of error?
(a) 1%
(b) 2%
(c) 3%
(d) 5%
(e) 10%

Choose the correct answer below:

Correct option is A

A,B,C and D only

The question asks about the significance levels (levels of error) at which a relationship between two quantitative or qualitative variables is considered statistically significant according to the Chi-square (χ²) test.

Key Concepts:

• Chi-square (χ²) test: A statistical test used to determine if there is a significant association between two categorical variables.
• Significance level (alpha level, α): The probability of rejecting the null hypothesis when it is actually true (Type I error). Common significance levels are 0.05 (5%) and 0.01 (1%).

Analyzing the Options:

• A. 1%: This is a common and stringent significance level (α = 0.01).
• B. 2%: While possible, this is not a standard significance level.
• C. 3%: Similar to 2%, this is not a standard significance level.
• D. 5%: This is the most common significance level (α = 0.05).
• E. 10%: This is a less stringent significance level (α = 0.10).

Evaluating the Answer Choices:

Now, let's look at the answer choices provided:

1. A, B, C, and D only / केवल A, B, C, D: This is incorrect because B (2%) and C (3%) are not standard significance levels.
2. B, C, D, and E only / केवल B, C, D, E: This is incorrect for the same reasons as above (B and C are not standard).
3. A, C, D, and E only / केवल A, C, D, E: This is incorrect because C (3%) is not a standard significance level.
4. A, B, D, and E only / केवल A, B, D, E: This is incorrect because B (2%) is not a standard significance level.

The Correct Approach:

The correct answer should include the standard significance levels, which are 1% (A) and 5% (D). While 10% (E) is sometimes used, it's less common. The options provided do not perfectly reflect this.

However, the closest correct answer would be A, D, and E, but since E is also less common, the closest is A and D.

Therefore, the closest correct answer from the given options would be one that includes A and D. However, none of the answer choices perfectly match this. The most accurate answer would be that significance is typically determined at 1% and 5%.